Soil shear strength is crucial in geotechnical engineering. It determines how much stress soil can handle before failing. This concept is key for designing stable structures like foundations and slopes.

The Mohr-Coulomb failure criterion helps us understand when soil will fail under stress. It considers both cohesion and friction between soil particles. This model is widely used to predict soil behavior in various engineering applications.

Shear Strength in Geotechnical Engineering

Fundamentals of Shear Strength

• Shear strength represents the internal resistance of soil to deformation by shear stress
• Defines the maximum shear stress a soil can withstand before failure occurs
• Critical parameter in geotechnical engineering influences stability of structures (foundations, slopes, retaining walls)
• Composed of two main components
  • Cohesion (c)
  • Internal friction (φ)
• Varies depending on soil type and conditions

Factors Influencing Shear Strength

• Soil composition affects shear strength (clay minerals, organic content)
• Particle size distribution impacts strength (well-graded vs poorly-graded soils)
• Moisture content alters strength characteristics (dry vs saturated conditions)
• Density plays a role in strength development (loose vs dense states)
• Stress history influences behavior (normally consolidated vs overconsolidated soils)
• Effective stress concept accounts for pore water pressure effects
  • Total stress = effective stress + pore water pressure
  • Effective stress governs soil strength and deformation

Measurement and Application

• Laboratory tests determine shear strength parameters
  • Direct shear test measures strength along a predetermined failure plane
  • Triaxial compression test allows for controlled drainage conditions
• Field tests provide in-situ strength measurements (vane shear test, cone penetration test)
• Understanding shear strength enables
  • Prediction of soil behavior under loading
  • Design of safe, stable geotechnical structures (retaining walls, foundations)
  • Assessment of slope stability and landslide potential

Mohr-Coulomb Failure Envelope

Components and Representation

• Graphical representation of soil shear strength
  • Normal stress (σ) plotted on x-axis
  • Shear stress (τ) plotted on y-axis
• Typically represented as a straight line
  • Described by equation $τ = c + σ tan(φ)$
• Cohesion (c) appears as y-intercept
  • Represents inherent shear strength with no normal stress applied
• Friction angle (φ) determines slope of failure envelope
  • Represents angle of internal friction between soil particles
• Separates stress states causing failure (above line) from stable states (below line)

Variations in Failure Envelope

• Cohesionless soils (clean sands) have failure envelope passing through origin
  • Indicates zero cohesion
• Shape and position change with soil properties
  • Density affects slope (higher density increases friction angle)
  • Moisture content alters cohesion (saturation generally reduces cohesion)
• Curved failure envelopes occur in some soils
  • Reflects non-linear strength behavior at high stresses
• Residual strength envelope lies below peak strength envelope
  • Represents reduced strength after large displacements

Applying the Mohr-Coulomb Criterion

Mathematical Expression and Parameters

• Mohr-Coulomb failure criterion expressed as $τf = c + σf tan(φ)$
  • τf represents shear strength at failure
  • σf denotes normal stress at failure
• Determine cohesion (c) and friction angle (φ) through
  • Laboratory testing (direct shear, triaxial tests)
  • Empirical correlations based on soil classification
• Calculate maximum sustainable shear stress for given normal stress
• Applicable to both total stress and effective stress analyses
  • Use appropriate parameters for each case (c', φ' for effective stress)

Applications in Geotechnical Engineering

• Analyze stability problems in various scenarios
  • Slope stability assessment (factor of safety calculations)
  • Retaining wall design (active and passive earth pressures)
  • Foundation bearing capacity evaluation
• Undrained conditions for cohesive soils often assume φ = 0°
  • Simplifies equation to τf = cu (undrained shear strength)
• Used in numerical modeling of soil behavior (finite element analysis)
• Guides selection of soil improvement techniques
  • Increase density to enhance friction angle
  • Add cementing agents to improve cohesion

Limitations and Considerations

• Linear approximation may not capture all soil behaviors
  • Non-linear strength envelopes at high stresses
  • Stress-dependent friction angles in some soils
• Does not account for intermediate principal stress effects
  • Can lead to conservative estimates in some cases
• Time-dependent behavior not directly addressed
  • Creep and relaxation may require additional considerations
• Anisotropy effects may necessitate different strength parameters in various directions

Normal vs Shear Stress at Failure

Relationship and Visualization

• Mohr-Coulomb model establishes linear relationship between normal and shear stress at failure
• Slope of relationship defined by friction angle (φ)
• Normal stress increase leads to higher shear stress required for failure
  • Reflects frictional nature of soil behavior
• Cohesion intercept represents stress-independent strength contribution
  • Particularly significant in cohesive soils (clays)
• Mohr circles represent stress states
  • Failure envelope tangent to circles at critical stress combinations
• Failure occurs along plane inclined at angle of (45° + φ/2) to major principal stress direction

Advanced Analysis Techniques

• Stress path analysis predicts soil behavior under complex loading
  • Useful for simulating construction sequences
  • Helps understand stress history effects
• Critical state soil mechanics incorporates volume change behavior
  • Defines unique relationship between void ratio and stress at large strains
• Strain rate effects can modify strength parameters
  • Faster loading generally increases apparent strength
• Soil anisotropy may require different strength parameters in various directions
  • Bedded deposits often exhibit directional strength variations
• Stress history influences strength characteristics
  • Overconsolidation ratio affects both cohesion and friction angle